Random Number Generationin SAS

SAS function for common distributions

• PROBNORM(x)– returns the probability from the standard normal distribution

• PROBBNRM(x,y,r)– standardized bivariate normal distribution

• POISSON(m,n)– returns the probability from a POISSON distribution

• PROBBNML(p,n,m)– returns the probability from a binomial distribution

• PROBCHI(x,df<,nc>)– returns the probability from a chi-squared distribution

• PROBF(x,ndf,ddf<,nc>)– returns the probability from an F distribution

• PROBT(x,df<,nc>)– returns the probability from a Student's t distribution

Random number generation

• How to randomly draw one observation according to a distribution?

• Pseudo random variables are numbers generated by a computer algorithm to simulate– Commonly used in Monte Carlo simulation– real random numbers.

• SAS has built in functions that generate pseudo random variables from several standard distributions.

• The algorithm used by SAS to produce these pseudo random variables , must be provided with an initial seed.

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Uniform distribution

• UNIFORM(SEED) - generates values from a random uniform distribution between 0 and 1

DATA random1; x = UNIFORM(-1); IF x>.5 THEN coin = 'heads'; ELSE coin = 'tails';RUN; PROC PRINT DATA=random1; VAR x coin;RUN;

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The statements if x>.5 then coin = 'heads' and else coin = 'tails' create a random variable called coins that has values 'heads' and 'tails'. The data sets random1 uses a seed value of -1. Negative seed values will result in different random numbers being generated each time.

Ranuni() also works!

Normal distributionNORMAL(SEED) - generates values from a random normal

distribution with mean 0 and standard deviation 1 DATA random2; x = UNIFORM(-1); y = 50 + 3*NORMAL(-1); IF x>.5 THEN coin = 'heads'; ELSE coin = 'tails';RUN;

PROC PRINT DATA=random2; VAR x y coin;Run;

5Rannor() also works!

Seed• Sometimes we want to generate the same set of random

numbers so that we can debug our programs or compare models. – We use the same number as the seed value. – The data sets random3 illustrates how to generate the same results each

time.

data random3; x = UNIFORM(123456); y = 50 + 3*NORMAL(123456); IF x>.5 THEN coin = 'heads'; ELSE coin = 'tails';RUN; PROC PRINT DATA=random3; VAR x y coin;RUN;

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Generating multiple runs, get statistics

DATA random4; DO i=1 to 100; x = UNIFORM(123456); IF x>.5 THEN coin = 'heads'; ELSE coin = 'tails'; OUTPUT; END;RUN; PROC FREQ DATA=random4; table coin;RUN;

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Cumulative CumulativeCOIN Frequency Percent Frequency Percent---------------------------------------------------heads 48 48.0 48 48.0tails 52 52.0 100 100.0

Getting Statisticsproc univariate data=random4 plot ;var x ; run;

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Other common distributions

• Exponential – RANEXP()• Binomial – RANBIN(seed,n,p)– returns a random variate from a binomial

distribution• Poisson - RANPOI(seed,m)– returns a random variate from a Poisson

distribution• Gamma distribution – RANGAM()

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Simulate student’s t-distributionsdata student ; seedz = 314159 ; seedw = 271828 ; array zz[40] _TEMPORARY_ ; array ww[40] _TEMPORARY_ ; do r=1 to 1000 ; sum_z = 0 ; sum_zsq = 0 ; sum_w = 0 ; sum_wsq = 0 ; do i=1 to 40 ; zz[i] = rannor(seedz) ; ww[i] = ranexp(seedw)-1 ; sum_z = sum_z + zz[i] ;sum_zsq = sum_zsq + zz[i]*zz[i] ; sum_w = sum_w + ww[i] ; sum_wsq = sum_wsq + ww[i]*ww[i] ; end ; t_z = sum_z/sqrt(40)/sqrt((sum_zsq-sum_z*sum_z/40)/39); t_w = sum_w/sqrt(40)/sqrt((sum_wsq-sum_w*sum_w/40)/39) ; output ; end ;title 'SIMULATED T FOR NORMAL AND EXPONENTIAL DATA';proc univariate data=student;var t_z t_w ;run;

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Cont’dproc gchart data=student ;title "Histograms for LOGBILI" ;vbar t_w / LEVELS=30 type=percent;RUN ;

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